b Evaluate the function for values of θ in the given interval.
A
a u= tan θ
B
b u starts at 0 and increases without bound.
Practice makes perfect
a We know that the coefficient of static friction u can be found using the given equation.
uWcos θ = W sin θ
We will suppose that W is the weight of a book that is lying on a ramp inclined at an angle θ. Next, we will solve this equation for u.
Now, we will recall the Tangent Identity.
tan θ = sin θ/cos θ
We can use this identity to continue simplifying the given expression. Let's do it!
u= sin θ/cos θ
⇒
u= tan θ
b We want to find what happens to the value of u when the angle increases from 0^(∘) to 90^(∘). To do so, we will use the equation found in Part A.
u= tan θ
Now, we will evaluate this equation for a few values of θ in the given interval. Let's start with θ= 30^(∘).
